*To view the video, click
the title of each lecture.
Date:
Tuesday, 18th March 2025, 09:00-10:00 TST
(GMT+8) , online on Zoom Speaker:Dr.
Nicolau S. Aiex (National Taiwan Normal University) Title: Quantitative estimates on singularities
of minimal hypersurfaces Abstract: We will discuss the
occasionally unavoidable presence of singularities on
minimal hypersurfaces in high dimensional ambient spaces and
estimates on its size. This is seemingly an analysis problem
but the variational notion of minimal hypersurfaces plays a
much more important role than its defining PDE. The proof
relies simply on coverings arguments by suitable open sets
and we will go over the main ideas and consequences.
Date: Tuesday, 25th March 2025,
09:00-10:00 TST (GMT+8) , online on Zoom Speaker:Dr.
Myles Workman (National Taiwan Normal University) Title: Minimal hypersurfaces: bubble convergence and index
Abstract: The regularity theories of Schoen--Simon--Yau and Schoen--Simon for stable minimal hypersurfaces are foundational in geometric analysis. Using this regularity theory, in low dimensions, Chodosh--Ketover--Maximo, and Buzano--Sharp, studied singularity formation along sequences of minimal hypersurfaces through a bubble analysis.
I will review this background, before talking about my recent work in this bubble analysis theory. In particular I will show how to obtain upper semicontinuity of index plus nullity along a bubble converging sequence of minimal hypersurfaces.
Date: Tuesday, 1st April 2025,
09:00-10:00 TST (GMT+8) , online on Zoom Speaker:Dr.
Zane Li (North Carolina State University) Title: Mixed norm decoupling for paraboloids
Abstract: In this talk we discuss mixed
norm decoupling estimates for the paraboloid. One motivation
of considering such an estimate is a conjectured mixed norm
Strichartz estimate on the torus which essentially is an
estimate about exponential sums. This is joint work with
Shival Dasu, Hongki Jung, and José Madrid.
Tuesday, 8th April 2025,
09:00-10:00 TST (GMT+8) , in Room M210 in NTNU Gongguan Campus
Mathematics Building, also online on ZoomSpeaker:Dr. Alan Chang (Washington
University in St. Louis) Title: Venetian blinds, digital sundials, and
efficient coverings Abstract: Davies's efficient covering
theorem states that we can cover any measurable set in the plane by
lines without increasing the total measure. This result has a dual
formulation, known as Falconer's digital sundial theorem, which
states that we can construct a set in the plane to have any desired
projections, up to null sets. The argument relies on a Venetian
blind construction, a classical method in geometric measure theory.
In joint work with Alex McDonald and Krystal Taylor, we study a
variant of Davies's efficient covering theorem in which we replace
lines with curves. This has a dual formulation in terms of nonlinear
projections.
Date:
Tuesday, 15th April 2025,
09:00-10:00 TST (GMT+8) , online on Zoom Speaker:
Dr. Bochen Liu (Southern University of Science and
Technology) Title: TBA
Abstract: TBA
Date: Tuesday, 29th April 2025,
15:00-16:00 TST (GMT+8) , in Room M210 in NTNU Gongguan
Campus Mathematics Building
Speaker:
Dr. Luca Gennaioli (University of Warwick)
Title:On the Fourier transform
of BV functions Abstract:
This talk is based on a
joint work with Thomas Beretti (SISSA, Trieste). The plan is
to introduce BV functions and the Fourier transform and
study how this two objects interact. We will prove
asymptotic formulae for the Fourier transform of BV
functions and (as a corollary) for characteristic functions
of sets of finite perimeter. Finally we will show how, using
techniques of geometric measure theory, it is possible to
sharpen some results of Herz, concerning convergence
properties of the Fourier transform of sets. Time
permitting, we will show some applications to the
isoperimetric inequality and some open problems.
Date: Tuesday, 6th May 2025, 09:00-10:00 TST (GMT+8) ,
in Room M210 in NTNU Gongguan Campus Mathematics Building Speaker:Dr.
Polona Durcik (Chapman University) Title: On
trilinear singular Brascamp-Lieb forms Abstract:
Brascamp-Lieb forms are multilinear integral forms acting
on functions on Euclidean spaces. A necessary and sufficient
condition for their boundedness on Lebesgue spaces is known.
Singular Brascamp-Lieb forms arise when one of the functions
in a classical Brascamp-Lieb form is replaced by a singular
integral kernel. Examples include Coifman-Meyer multipliers
and multilinear Hilbert transforms. A general necessary and
sufficient condition for the boundedness of singular
Brascamp-Lieb forms remains unknown, and their theory
continues to be developed on a case-by-case basis. In this
talk, we classify all trilinear singular Brascamp-Lieb forms
and establish bounds for a specific class of forms that
naturally emerge from this classification. Additionally, we
provide a survey of the literature and briefly discuss
conditional bounds for forms associated with mutually
related representations. This talk is based on joint work
with Lars Becker and Fred Yu-Hsiang Lin.
Date: Tuesday, 13th May 2025, 09:00-10:00 TST
(GMT+8) , in Room M210 in NTNU Gongguan Campus Mathematics Building
Speaker:Dr. Hitoshi
Tanaka (Tsukuba University of Technology)
Title: Multilinear embedding theorem for fractional sparse operators Abstract:
Under \( A_{\vec{p}} \) condition for weights, we show some simple sufficient conditions for which the multilinear embedding theorem holds for fractional sparse operators. Checking this simple sufficient condition, we demonstrate that theorem for power weights.
Date: Tuesday, 13th May 2025,
10:00-11:00 TST
(GMT+8) , in Room M210 in NTNU Gongguan Campus Mathematics Building
Speaker:Dr. Hiroki Saito
(Nihon University)
Title:Infinitesimal \( L^p \rightarrow L^q \) relative bounds for \( (-\Delta)^{\alpha/2} + v \)
Abstract:
By analyzing the trace inequality for Bessel potentials, some Morrey-type sufficient conditions are given for which
\( L^p \rightarrow L^q \), \( 1 < p, q < \infty \), infinitesimal relative boundedness of the Schrödinger operators
\( (-\Delta)^{\alpha/2} + v \) holds. These results provide new aspects of Morrey spaces and a nice application of
weight theory. This is a joint work with Prof. N. Hatano, R. Kawasumi and H. Tanaka.